"We have an agreement with the player," Galliani revealed to Sky Sport 24.
Nevertheless, Milan have yet to reach an all-important deal with Tevez's current club City, although
Galliani has confirmed that his side are aiming to sign Tevez on loan with a view to a permanent move.
"There are ongoing negotiations with Manchester City and we expect an answer on a loan proposal with the right to purchase the player later on very soon," he added.
Galliani also put a triumphant end to all speculation surrounding Brazilian schemer Alexandre Pato's mooted departure to moneybags Paris Saint-Germain.
PSG are rumored to be keen on snagging Pato to the French capital following their appointment of former Milan chief Carlo Ancelotti as the club's new trainer.
"There is no negotiation for the sale of Pato," Galliani added.
Milan will resume their domestic Serie A schedule when they tackle Atalanta on Sunday.